Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)

Second Order Transitions in Quantum-Classical Molecular Dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-3805
  • Mixed quantum--classical models have attracted considerable interest due to the expectation that they correctly describe non--adiabatic processes of full quantum dynamics. One of these models, the so--called QCMD model, represents most degrees of freedom of the molecular system by the means of classical mechanics but an important, small portion of the system is modeled by a wavefunction: the wavefunction is nonlinearly coupled to the classical motion via a singularly perturbed Schrödinger equation. In extension to the analysis given by F.A.~Bornemann [{\em Homogenization in Time of Singularly Perturbed Mechanical Systems}, Lecture Notes in Mathematics, no.~1687, 1998, Springer, Berlin], the article presents an asymptotic expansion up to second order in the perturbation parameter. This result allows for the construction of new models and numerical integration schemes.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Metadaten
Author:Peter Nettesheim
Document Type:ZIB-Report
Tag:asymptotics; mixed quantum-classical models; quantum populations; quantum-classical molecular dynamics
MSC-Classification:41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q20 Semiclassical techniques, including WKB and Maslov methods
Date of first Publication:1998/12/21
Series (Serial Number):ZIB-Report (SC-98-37)
ZIB-Reportnumber:SC-98-37
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.